I have a copper field but it is across a small lake and all my other mats are on the opposite side so I was wondering instead of running back and forth now that I have electric can I transport or convey the copper to my side either across or under the water?

Underground Belts allow you to move items across small (4 squares or less) channels, but otherwise you have to detour around the water. Belts work independent of power though, so you can use them to transport ores even if you are using burners.